On band circulant matrices in the periodic spline interpolation theory
type: Item
instance of: scholarly article
title: On band circulant matrices in the periodic spline interpolation theory
zbMATH Open document ID: 0584.41004
DOI: 10.1016/0024-3795(85)90153-3
author: F. Dubeau
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The interpolation of a periodic function by a periodic spline of degree n with equal intervals requires the solution of a linear system \(C_ ns=b\), where \(s,b\in {\mathbb{R}}^ N\) and \(C_ n\) is a band circulant matrix of order \(N\geq n\). When n is odd, \(C_ n\) is always invertible, and it is known [\textit{D. Kershaw}, J. Inst. Math. Appl. 20, 227-228 (1977; Zbl 0374.65006)] an explicit bound for \(\| C_ n^{-1}\|\). When n is even, \(C_ n\) is invertible if and only if N is odd. The author extends the method developed by D. Kershaw to the even case. He uses a regular transformation E to obtain \(s=(EC_ n)^{-1}Eb\), decomposes \(EC_ n\) into a product of strictly diagonally dominant circulant tridiagonal matrices and obtains an explicit bound for \(\| (EC_ n)^{-1}\|\) (when n is even and N is \(odd>n)\).
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 3935658
zbMATH Keywords: periodic spine
zbMATH Keywords: band circulant matrix
reviewed by: Radu Precup
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90153-3
OpenAlex ID: W2002469980
cites work: Q5540873
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cites work: Q3208805
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description: scientific article; zbMATH DE number 3935658